论文标题
Szasz-Mirakjan类型操作员对关联的GBS运营商的近似
Approximation of associated GBS operators by Szasz-Mirakjan type operators
论文作者
论文摘要
在本文中，研究了Szasz-Mirakjan类型运算符的近似属性以达到两个变量的函数，并根据总和连续性模量确定双变量算子的收敛速率。相关的GBS（广义布尔总和） - 双变量szasz-mirakjan型运算符的形式被认为是两个变量的函数，以在Bogel的空间中找到B-连续和B-差异函数的近似值。此外，根据属于Lipschitz类的平滑度和功能的混合模量，发现了GBS类型运算符的近似程度，并根据Peetre k函数获得了开创性的结果。最后，通过图形表示有限和无限总和来检查双变量Szasz-Mirakjan类型运算符和相关GBS类型操作员的收敛速率，这表明相关GBS类型操作员的收敛速率比Bivariate Szasz-Mirakjan类型运算符更好。
In this article, the approximation properties of the Szasz-Mirakjan type operators are studied for the function of two variables, and the rate of convergence of the bivariate operators is determined in terms of total and partial modulus of continuity. An associated GBS (Generalized Boolean Sum)-form of the bivariate Szasz-Mirakjan type operators are considered for the function of two variables to find an approximation of B-continuous and B-differentiable function in the Bogel's space. Further, the degree of approximation of the GBS type operators is found in terms of mixed modulus of smoothness and functions belonging to the Lipschitz class as well as a pioneering result is obtained in terms of Peetre K-functional. Finally, the rate of convergence of the bivariate Szasz-Mirakjan type operators and the associated GBS type operators are examined through graphical representation for the finite and infinite sum which shows that the rate of convergence of the associated GBS type operators is better than the bivariate Szasz-Mirakjan type operators.
